Explanation for Question 6 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question six gives us this picture and reads the circle above has center. 2 Oh, the length of arc ADC is five PI and X is equal to 3 100. What is the length of arc? 4 ABC? Okay. 5 So let's draw out the information that we're given on this figure. 6 We know that the length of arc ADC, 7 so this segment right here is going to be equal to five PI. 8 We also know that X, so this angle right here is going to be 9 equal to 100 degrees, and 10 then they ask the length of arc ABC. 11 So arc ABC is going to be this other portion of the 12 circle. We can solve this problem with the knowledge that 13 the ratio of two angles in the same circle is equivalent to the ratio 14 of their arc length. So let's first find the angle 15 or the measurement of this angle right here. 16 We know that the angle or the angles of a whole circle is going 17 to be equal to 360 degrees. 18 So 360 degrees is the whole circle. 19 And we have that. This segment is 100 degrees. 20 So the length or excuse me, the measurement of this angle is going to 21 be 360 degrees. 22 Minus 100 degrees is equal to 260 degrees. 23 So this angle measurement is 260 degrees. 24 Now let's set up that ratio that I was talking about. 25 So we have 100 degrees over 260 degrees, 26 and now we want to set up a ratio of their arc lengths. 27 So from 100 degrees, we had a length of five PI and 28 we're trying to solve for the length of ABC, 29 which is what has the 260 degree angle measurement. 30 So let's just call that X for now, and then we can cross multiply 31 and solve through to get the value of X. 32 So we have 100 times X is equal to 260 times five 33 PI Scott, 100 X on one side, 34 and we have five PI times two 60. 35 So five times two 60 is 1300. 36 So we have 1300 PI. Now let's divide both sides by 100 37 and we get that X is equal to 13 PI. 38 So the length of arc ABC, 39 this arch right here is equal to 13 PI B.